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Research Article  |   May 2010
Functional frameworks of illumination revealed by probe disk technique
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Journal of Vision May 2010, Vol.10, 6. doi:10.1167/10.5.6
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      Alan L. Gilchrist, Ana Radonjić; Functional frameworks of illumination revealed by probe disk technique. Journal of Vision 2010;10(5):6. doi: 10.1167/10.5.6.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

We used a novel probe disk technique to test for the existence of functional frames of reference for lightness perception in complex images. Thirteen identical gray disks were electronically pasted into the photograph Trastevere, which shows two large regions of sunlight and shadow. Observers matched the lightness of each disk with a Munsell scale. The data revealed a framework effect. That is, lightness differences within either the sunlight or shadow region were small relative to the pronounced step function at the framework boundary. Additional experiments testing the perceived embeddedness of the disks showed that the framework effect was increased when disk size and shape were altered to conform to the perspective shown in the photograph and when the disks were blurred slightly to conform to the graininess of the photograph. The effect was further increased when the photograph was viewed through a pinhole and when the disks were presented one by one. The effect was reduced when paper disks of equal luminance and visual angle were pasted onto the glass front of the CRT screen. When the sunlight framework was covered with black paper, the remained disks within the shadow region appeared white, as predicted by the anchoring theory (A. Gilchrist, 2006).

Introduction
Lightness, or the perceived shade of gray of a surface, corresponds to the reflecting capacity of the object surface, called reflectance (white reflects 90%; black 3%). The basic problem in human lightness perception arises because the intensity of the light reflected from a surface to the eye (called luminance) depends on both its reflectance and the intensity of light illuminating it. Because of this, the luminance of a surface tells you nothing about its reflectance, as any luminance can come from any shade of gray. Helmholtz (1866/1924) suggested that, in order to derive surface lightness, the visual system takes into account the amount of illumination reaching the surface but he did not specify how this is done. A more operational approach can be found in the anchoring theory (Gilchrist, 2006; Gilchrist et al., 1999), which incorporates the key insight that the visual system does not need to know how much illumination a surface is getting—it only needs to know which surfaces are getting the same amount of illumination. Thus, if the visual system can group together surfaces that receive the same illumination, it can compute their lightness values simply by comparing the luminances of those surfaces, with no further reference to the illumination. A group of image regions representing surfaces under common illumination can be regarded as a frame of reference, as suggested earlier by Koffka (1935). According to this gestalt approach, the retinal image is perceptually segmented into different frames of reference (frameworks), typically representing different levels of illumination. 
In the research reported here, we tested the existence of functional frames of reference within a complex image using a novel technique for probing the computation of lightness at arbitrary positions in the image. Since the technique was first introduced by Gilchrist and his collaborators (Gilchrist & Radonjic, 2005), it has already been adopted by several laboratories (Bressan, 2006; Hillis & Brainard, 2007; Shapiro, Smith, & Knight, 2007). Small gray disks, each with the same standard luminance, are pasted into the image of a scene with complex illumination. The perceived lightness of each disk, quantified by observer matches to a standard scale, reveals the value computed by the visual system for that test luminance at that location in the image, much as the gauge figure of Koenderink, Van Doorn, and Kappers (1992) reveals the perceived surface orientation at any arbitrary location in an image. When computed lightness for a standard luminance value is probed at multiple locations in an image, a map emerges showing areas within which computed lightness values are relatively homogeneous and locations where these values shift. By discovering where within an image the computed lightness value of a standard luminance changes, the probe disk technique can reveal those features of the image to which the visual system is most sensitive. If a region of the retinal image representing a field of illumination functions as a frame of reference for lightness, we would expect that probe disks pasted into that region of the image would appear to have roughly the same lightness value, and that lightness variations due to local background luminance would be small relative to variations from one framework to the next. If the region does not function as a frame of reference, probe disk appearance would correlate with some other metric, like disk/background luminance ratio, without regard to framework location. 
Our main goal was to test the validity of the framework concept, in addition to other predictions based on the anchoring theory. Thus, a brief summary of the basic components of the anchoring theory will provide the necessary context for our experiments. 
Segmentation of frameworks
Frameworks in the retinal image represent regions of common illumination. They are the products of both grouping and segmentation, which are just two sides of the same coin. The grouping factors include most of the gestalt grouping principles, such as similarity, proximity, and good continuation. However, this grouping, for lightness computation, must be distinguished from the more familiar use of grouping principles in the perceptual organization of objects, in which image regions are often grouped by common reflectance rather than common illumination. Two strong segmentation factors serve as framework boundaries: fuzzy boundaries (that is, penumbrae) and depth boundaries (including both corners and occlusion boundaries). 
Provisional computation within a framework
The highest luminance within a framework is assigned the value of white. Lightness values for the darker regions depend simply on the ratio between the luminance of the region and the highest luminance, using the formula Lightness = (Lt/Lh * 90%), where Lt is the luminance of the target region, Lh is the highest luminance in the framework, and 90% is the reflectance of white. When a single framework fills the entire visual field (as when your head is placed within a hemisphere painted on its interior with a simple pattern that contains no grouping factors), these provisional values are also the final perceived values. However, in complex images, containing multiple frameworks, another factor is engaged. 
Codetermination
In complex images, each patch is a member of at least two frameworks: a global framework consisting of the whole visual field, and one or more local frameworks. The final perceived lightness value for the patch is a weighted average of the values computed for that patch within both its local framework and the global framework. The weighting depends on the size of the local framework and the number of elements it contains. 
To test the validity of the framework concept as well as other predictions of the anchoring theory, we used as a test image, a wonderful photograph, Trastevere (1959), by the late French photographer Henri Cartier-Bresson ( Figure 1), which shows a courtyard in Rome divided into two large regions of sunlight and shadow. We will refer to these regions as local frameworks and we will refer to the whole image as the global framework. We inserted a probe disk at 13 different locations in the image, both in sunlight and in the shadow, to probe lightness computation at each location. 
Figure 1
 
The reproduction of the photograph Trastevere (1959) by Henri Cartier-Bresson. Thin brackets on the side indicate the part of the image used as stimulus in Experiments 1, 3, 4, and 5. Bold brackets indicate the part of the image used as stimulus in Experiment 2.
Figure 1
 
The reproduction of the photograph Trastevere (1959) by Henri Cartier-Bresson. Thin brackets on the side indicate the part of the image used as stimulus in Experiments 1, 3, 4, and 5. Bold brackets indicate the part of the image used as stimulus in Experiment 2.
Experiment 1. Increasing embeddedness: Identical, perspective, and blurred disks
In our first experiment, we varied the perceived embeddedness of the disks, which we will define as the degree to which each of the 13 probe disks appeared to be a part of the original scene that was photographed. Across three conditions, the perceived embeddedness of the disks was systematically increased. In the identical condition, the disks were identical and round, with sharp edges. In the perspective condition, we changed the size and shape of the disks to conform to the depth and slant of the background surface in the photograph. In the blurred condition, we added a slight blur to the disk edges to conform to the graininess of the photograph. 
We derived three predictions from the anchoring theory. First, we predicted that all the disks within an illumination framework, either sunlight or shadow, would appear similar in lightness, with a prominent lightness shift between frameworks. Due to the role of weaker grouping principles mentioned earlier, we did not predict that lightness values would be identical within a framework. Rather we predicted that lightness differences within a framework would be small relative to the lightness shift at the framework boundary. This pattern of results will be labeled a framework effect, and we will define the size of the framework effect as the difference between the average lightness of disks in one framework and those in an adjacent framework. 
Second, we predicted that the greater the perceived embeddedness of the disks, the larger the framework effect. In the global framework, all disks have the same lightness value and the framework effect is zero. The more strongly each disk is perceptually grouped with its local framework, the greater the weight of the local lightness value for each disk (at the expense of its global value). As local values get more weight, the difference between the value of the disks in the different frameworks, that is, the framework effect, increases. 
Third, the combination of local and global values predicts that differences in the magnitude of the framework effect will show up in the shadowed region, not the sunlight region, of the photograph. The reason for this prediction can be simply described. The sunlight region has the same highest luminance as the global framework, whereas the highest luminance in the shadowed framework is much lower than the highest luminance in the global framework. Thus, the more a disk in the shadow appears embedded within that framework, the lighter it should appear, as its local value gains more weight in the computation of the final lightness value. 
Methods
Distal stimulus
We began by conducting a pilot study using a relatively low resolution version of the image and we varied perceived embeddedness by varying the resolution of the probe disks. To replicate that lower resolution pilot image, we first scanned a reproduction of the original photograph Trastevere by Cartier-Bresson in 300 dpi resolution (see Figure 1) and then adjusted the levels, brightness, and contrast in the scanned image using Adobe PhotoShop software (AdobeSystems, CA, USA). This allowed us to vary the degree to which the disks appear as embedded in the scene by varying both the resolution and perspective of the probe disks. We selected a part of the photograph (marked by thin brackets in Figure 1) in which half of the scene was in sunlight while the other half was in shadow. We then pasted identical gray probe disks at 13 different locations (shown in Figure 2) in the image: 6 in the sunlight and 7 in the shadowed region. 
Figure 2
 
A schematic representation (not the actual stimulus) showing the locations of 13 probe disks on the photograph.
Figure 2
 
A schematic representation (not the actual stimulus) showing the locations of 13 probe disks on the photograph.
We varied the degree of perceived embeddedness of the disks across three conditions. In the identical condition, the disks were created and pasted on the image using Microsoft PowerPoint 2004 software (Microsoft, WA, USA). All disks were identical in shape (perfectly circular), size (0.9 cm in diameter), and luminance (approximately 14.4 cd/m 2) with sharp edges (part of the stimulus shown in Figure 3a). 
Figure 3
 
A sample of the stimulus showing (a) identical, (b) perspective, and (c) blurred probe disks.
Figure 3
 
A sample of the stimulus showing (a) identical, (b) perspective, and (c) blurred probe disks.
In the perspective condition, the shape and size of each disk were altered to conform to the linear perspective of the image (but only roughly, being done manually in PowerPoint): disks placed on nearer walls were enlarged, those placed on farther walls were reduced in size and disks located on slanted walls were compressed to match the slant of the walls ( Figure 3b). 
In the blurred condition ( Figure 3c), the disks were created and pasted using Adobe Photoshop software. They were identical to those in the perspective disk condition except that the edges of each disk were blurred slightly to match the graininess of the photograph (PhotoShop function: “feather; 1 pt”). 
Laboratory arrangements
The stimuli were displayed at a resolution of 1152 × 870 pixels on a 20″ Apple Multiple Scan CRT monitor (38 × 29 cm in size), resting on a desk in an otherwise dark room. The image filled in the entire screen and its center was 112 cm above the floor. The observer was seated in a chair in front of the screen and viewed the display at a distance of 65 cm. 
Proximal stimulus
At the viewing distance of 65 cm, each disk in the identical condition subtended 0.8° of visual angle and the entire image subtended 32.5° horizontally and 25° vertically. Photometric measurements were taken using a Konica Minolta LS-100 luminance spot meter. The average luminance of the disks was 14.4 cd/m 2. With the exception of the disk at position 10 (luminance 13.5 cd/m 2), all disks were practically equiluminant, within the measurement error (±2%) of the photometer. The highest luminance on the screen was 57.2 cd/m 2, the luminance range was 13:1, and the luminance ratio at the illumination boundary in the image was 5.2:1. 
Matching chart
Matching was done using a Munsell chart, housed in a metal chamber positioned to the right of the monitor and separately illuminated by a 15-W fluorescent tube mounted 10 cm above the chart. The chart consisted of 16 chips, 1 cm × 3 cm each, mounted on a white background. The chips on the chart were arranged in ascending reflectance order: from black, equivalent to Munsell 2.0 to white, equivalent to Munsell 9.5, with 0.5-step intervals. The luminance of the white chip was 360 cd/m 2
Instructions
The observer was seated and asked to “pick a chip from this scale (pointing to the Munsell scale) that matches the shade of each disk”. 
Observers
A separate group of 15 observers matched the lightness of the disks (in no particular order) in each condition. 
Criteria for exclusion
Throughout all experiments, observer responses that fell more than 3 standard deviations above or below the mean of the whole group in a given condition (excluding the compared match) were designated as outliers and excluded from the data analysis. 
Results and discussion
For the purposes of data analysis, all Munsell matches were converted into log reflectance. The mean lightness match for each disk (in log reflectance) is shown in Figure 4. For each condition, we computed (1) the average lightness for the 6 disks in the sunlight framework, (2) the average lightness for the 7 disks in the shadow framework, and (3) the framework effect, defined as the difference between the sunlight average and the shadow average. 
Figure 4
 
Experiment 1: Lightness of each probe disk in the identical (solid line), the perspective (dashed line), and the blurred (dotted line) conditions. Disk numbers correspond to locations marked in Figure 2.
Figure 4
 
Experiment 1: Lightness of each probe disk in the identical (solid line), the perspective (dashed line), and the blurred (dotted line) conditions. Disk numbers correspond to locations marked in Figure 2.
A repeated measures analysis of variance (ANOVA) with condition (identical vs. perspective vs. blurred) as a between-subjects factor and framework (sunlight vs. shadow) as a within-subjects factor revealed a significant main effect of framework, F(1, 42) = 344.10, p < 0.001. Overall, the disks in the sunlight were perceived as darker ( M = 1.12, SE = 0.02) than the disks in the shadow ( M = 1.61, SE = 0.02). The Framework × Condition interaction, F(2, 42) = 3.16, p = 0.05, was marginally significant. 
To explore further this interaction, two separate ANOVAs compared the average lightness of the disks in each framework across conditions. While condition had no effect on lightness of the disks in the sunlight, the effect on disks in the shadow was marginally significant, F(2, 42) = 3.02, p = 0.06. Planned comparisons (Tukey HSD) revealed that the disks in shadow were significantly lighter in the blurred than in the perspective condition ( p < 0.05). 
In a separate one-way ANOVA, we compared the size of the framework effect across conditions and found a marginally significant effect, F(2, 42) = 3.17, p = 0.05. Planned comparisons (Tukey HSD) showed that the framework effect was significantly larger in the blurred condition (0.58 log reflectance, equivalent to 3.2 Munsell units) than in the identical condition (0.42 log reflectance, equivalent to 2.25 Munsell units; p < 0.05). The difference between identical and perspective conditions (0.42 vs. 0.49 log reflectance, respectively) and perspective and blurred conditions (0.49 vs. 0.58 log reflectance), though in the predicted direction, did not reach significance. 
Figure 4 reveals three main features of the data. First, there is a pronounced framework effect. Variations in disk lightness within a framework are small relative to the prominent step function at the framework boundary. Disks 1 and 4, on darker backgrounds, appeared lighter, suggesting a local contrast effect, but this suggestion is seriously undermined by the demonstration in Figure 9. Second, the framework effect becomes successively stronger as perceived embeddedness increases, that is, as the disks are made increasingly similar to their scene locations in perspective and sharpness. Third, these differences show up in the shadow framework not the sunlight framework, as predicted. 
Experiment 2. Reducing embeddedness: Paper disks
Our goal in Experiment 2 was to reduce, rather than increase, the perceived embeddedness of the disks and thus reduce the size of the framework effect. 
Thus, actual paper disks were pasted onto the glass of the CRT monitor. To create the disks for this paper condition, white paper was first bonded onto opaque black contact paper (to prevent light coming through the paper from the computer screen). Then disks were punched out using a round paper punch, 0.6 cm in diameter. Because the paper disks were slightly smaller than those (0.9 cm) in the identical condition of Experiment 1, to keep relative sizes constant, the image was zoomed out by approximately 30% and included a larger portion of the scanned photograph, indicated by the bold brackets in Figure 1. The stimulus image was 29 × 30 cm in size and centered on the CRT screen. The visible portion of the screen that was not filled with the image (approximately 6 cm on each side) was covered with black color-aid paper. 
Experiment 2 included a control condition that was equivalent to the identical condition of Experiment 1 in all respects except that the image was zoomed out to match the paper condition. 
To make the disks in the paper condition completely identical in both luminance and color to those in the control condition (and Experiment 1), the screen was additionally illuminated by two 15-W florescent bulbs that flanked the screen on the left and the right. Relative to the screen, each bulb was mounted in a vertical position, centered on the horizontal midline, 50 cm forward of the screen, and 37 cm off the vertical midline (left and right, respectively). These symmetrical lateral bulb positions provided two advantages: (1) they prevented any visible reflection of the bulbs on the screen and (2) the slight luminance gradient due to the eccentric position of each bulb was largely canceled out by the other. The bulbs were mounted on a wooden frame that rested on the floor and could be moved toward and away from the screen until the luminance of the paper disks was precisely equal to that of the disks embedded in the electronic image. The chromaticity of the disks was equated using colored filters, with 53% of each bulb wrapped with Rosco filter No. 64A Blue and 10% of each bulb wrapped with RoscoLux filter No. 89 Moss Green. Black paper baffles attached to the sides of the bulbs kept them out of the observer's visual field. 
The observer viewed the stimulus binocularly through a horizontal slot (13 × 3 cm) in an occluding panel mounted on the wooden frame holding the bulbs. The slot was left/right centered with respect to the computer screen and positioned at 103-cm height. At the reduced viewing distance of 52 cm (compared to 65 cm in Experiment 1), each disk subtended 0.7° of visual angle (compared to 0.8° in Experiment 1) and the entire image subtended 31.2° horizontally and 32.2° vertically. 
Disk luminances in the paper condition and in the control condition were equal and equivalent to those in Experiment 1. A separate group of 15 observers viewed the stimulus in each condition and judged the lightness of each disk using the Munsell chart. 
Results and discussion
Mean lightness matches for each disk are shown in Figure 5. For both conditions, we computed the average lightness value of the disks in the sunlight and in the shadow framework as well as the framework effect. 
Figure 5
 
Experiment 2: Lightness of each probe disk in the paper (solid line) and the control (dashed line) conditions.
Figure 5
 
Experiment 2: Lightness of each probe disk in the paper (solid line) and the control (dashed line) conditions.
A repeated measures ANOVA with condition (paper vs. control) as a between-subjects factor and framework (sunlight vs. shadow) as a within-subjects factor revealed a significant main effect of framework, F(1, 28) = 161.65, p < 0.001. Like in Experiment 1, overall, the disks in the sunlight were perceived as darker ( M = 1.30, SE = 0.03) than the disks in the shadow ( M = 1.61, SE = 0.03). The Framework × Condition interaction was also significant, F(1, 28) = 9.27, p < 0.01. 
Planned comparisons explored further this interaction and showed that (1) the disks in the sunlight were darker than the disks in the shadow in both the paper condition, t(14) = 6.87, p < 0.001, and the control condition, t(14) = 11.10, p < 0.001, and (2) the disks in the sunlight were significantly darker in the control than in the paper condition, t(28) = 4.15, p < 0.001, while the disks in the shadow did not significantly differ across conditions. 
Finally, we compared the framework effect across conditions and found it was significantly larger in the control condition (0.4 log reflectance, equivalent to 2.1 Munsell units) than in the paper condition (0.24 log reflectance, equivalent to 1.5 Munsell units), t(28) = 3.05, p < 0.01. 
Figure 5 reveals that, as predicted, the framework effect was substantially weakened by the use of paper disks. In addition, the data show a general lightening of all the disks, in both frameworks, relative to the control condition. We interpret this pattern in the following way. All of the paper disks, being mounted on the glass front of the computer screen, appeared to float slightly in front of the image itself. This separate depth plane, slightly closer to the observer, altered the perceptual grouping of the disks in several ways. It caused the disks to appear less embedded in the sunlight and shadow frameworks and it caused all the disks to form their own perceptual group based on their coplanarity and their similarity in luminance and shape. These factors also caused the disks to appear more as paper objects in the general dim laboratory illumination. In this laboratory framework, which might be called super-global, the disks were equal to the highest luminance surfaces, and thus would have appeared white. We believe that the lightening of the disks is due to these two other groupings: the grouping of the disks among themselves and the grouping of the disks with the laboratory room. 
Experiment 3. Weakening the global framework: Pinhole vs. binocular viewing
Yoko Mizokami reminded us that viewing a photograph through a pinhole increases the perceived depth in the photograph. We hypothesized that the reduced sense of flatness would weaken the contribution of global anchoring and produce a stronger framework effect, primarily by lightening the disks in the shadow. The binocular (control) condition of Experiment 3 was identical to the blurred condition of Experiment 1 except that the stimulus was viewed through the horizontal slot in the occluding panel on the wooden frame, as in Experiment 2. In the pinhole condition, observers viewed the display monocularly through a pinhole in the occluding panel, centered relative to the computer screen at 108-cm height. 
Because we used the same zoomed-in image as in Experiment 1 but, due to an oversight, did not remove the black paper used in Experiment 2, the rightmost disk fell beyond the visible part of the image, leaving only 12 disks in the image (6 in the sunlight and 6 in the shadowed region of the image). 
To keep the visual angle of the disks approximately the same as in Experiments 1 and 2, the viewing distance was increased to 85 cm. Each disk subtended 0.6° of visual angle and the entire image subtended 19.4° horizontally and 20° vertically. Because of the increase in viewing distance, the position of the chamber with the Munsell chart was changed. It was moved to the observer's side of the occluding panel and was positioned on a stand, just to the right of the observer, at 80-cm height. 
A separate group of 15 observers viewed the stimulus in each condition and judged the lightness of each disk using the Munsell chart. One observer was excluded from the further analysis for being an outlier, which yielded a total of 14 observers in the binocular condition. 
Results
Mean lightness matches for each disk are shown in Figure 6. We computed the average lightness value of the disks in the sunlight and in the disks in the shadow as well as the framework effect for each condition. 
Figure 6
 
Experiment 3: Lightness of each probe disk in the pinhole (dashed line) and the binocular (solid line) conditions.
Figure 6
 
Experiment 3: Lightness of each probe disk in the pinhole (dashed line) and the binocular (solid line) conditions.
A repeated measures ANOVA with condition (binocular vs. pinhole) as a between-subjects factor and framework (sunlight vs. shadow) as a within-subjects factor revealed a significant main effect of framework, F(1, 27) = 286.44, p < 0.001. Like in Experiments 1 and 2, overall, the disks in the sunlight were perceived as darker ( M = 1.08, SE = 0.03) than the disks in the shadow ( M = 1.70, SE = 0.03). The Framework × Condition interaction was also significant, F(1, 27) = 10.63, p < 0.01. 
Planned comparisons explored further this interaction showing that (1) the disks in the sunlight were darker than the disks in the shadow in both the binocular condition, t(13) = 13.73, p < 0.001, and the pinhole condition, t(14) = 11.92, p < 0.001, and (2) the disks in the sunlight were significantly darker in the pinhole condition than in the binocular condition, t(38) = 2.91, p < 0.01, while the disks in the shadow did not significantly differ across conditions. 
Most relevant to our hypothesis, the framework effect was significantly larger in the pinhole condition (0.75 log reflectance, equivalent to 4 Munsell units) than in the binocular condition (0.51 log reflectance, equivalent to 2.9 Munsell units), t(27) = 3.26, p < 0.01. This difference was expressed primarily in the sunlight framework, contrary to our prediction. 
Experiment 4. Testing the disk group hypothesis: Successive vs. simultaneous presentation
When all disks are present in the image simultaneously, as they were in Experiments 13, we should expect all 13 disks themselves to form a weak perceptual group, or framework. In Experiment 2, such a disk grouping was created, we believe, based on the separate depth plane of the paper disks. However, even when paper disks are not used, we should expect the disks to be grouped together based on their similarity in luminance, size, and shape. Such an outcome is explicitly predicted by the anchoring theory, and several reports have been published supporting such a grouping effect (Agostini & Proffitt, 1993; Bonato, Cataliotti, Manente, & Reynolds, 2003). In that framework, the disks would all have the same lightness and it would be white. Such a weak perceptual group would show up in our data in two ways. First, the framework effect would be diluted because within the disk group framework, all disks would have the same lightness value. Second, all the disks would appear slightly lighter. 
To test these ideas, we decided to compare successive and simultaneous presentations of the disks. 
Methods
The simultaneous condition of Experiment 4 was identical to the perspective condition of Experiment 1 in all respects, with 20 observers. In the successive condition, a separate group of 20 observers viewed the disks one by one. Each observer saw the 13 disks in a different random order. Pressing the space key would remove the disk that was judged and replace it with the next one. 
Results
Mean lightness matches for each disk are shown in Figure 7
Figure 7
 
Experiment 4: Lightness of each probe disk in the simultaneous (solid line) and the successive (dashed line) conditions.
Figure 7
 
Experiment 4: Lightness of each probe disk in the simultaneous (solid line) and the successive (dashed line) conditions.
A repeated measures ANOVA with condition (simultaneous vs. successive) as a between-subjects factor and framework (sunlight vs. shadow) as a within-subjects factor revealed a significant main effect of framework, F(1, 38) = 242.07, p < 0.001. As in Experiments 13, overall, the disks in the sunlight were perceived as darker ( M = 1.27, SE = 0.02) then the disks in the shadow ( M = 1.67, SE = 0.02). The Framework × Condition interaction was also significant, F(1, 38) = 15.54, p < 0.001. 
Planned comparisons showed that (1) the disks in the sunlight were darker than the disks in the shadow in both the simultaneous condition, t(19) = 9.21, p < 0.001, and the successive condition, t(19) = 12.57, p < 0.001, and (2) the disks in the sunlight were significantly lighter in the simultaneous condition than in the successive condition, t(38) = 3.02, p < 0.01, while the disks in the shadow did not significantly differ across conditions. 
Finally, we found that the framework effect was significantly smaller in the simultaneous condition (0.30 log reflectance, equivalent to 1.9 Munsell units) than in the successive condition (0.50 log reflectance, equivalent to 2.9 Munsell units), t(38) = 3.94, p < 0.001. Thus, successive presentation of the disks increased the framework effect by one Munsell step. 
These results support our hypothesis that when all 13 disks are presented at the same time, they form a weak group. Within this group, all the disks, having the highest luminance, are computed as white (Gilchrist et al., 1999). When this effect is factored in, it tends to wash out the framework effect by lightening all of the disks. In the absence of the disk group (that is, under successive viewing), the disks have local values of middle gray in the sunlight and white in the shadow. Factoring in the weak whitening of the disk group raises values more for the disks in the sunlight because they are darker in their local framework. 
Experiment 5: Lightness computation in the isolated shadow framework
Although according to the anchoring theory, the highest luminance in a local framework is assigned the value of white in that local framework, it will not appear white when its global value is factored in, as long as the highest luminance in the global framework is higher than the highest luminance in the local framework. This implies that if the sunlight framework were removed, the disks, which have the highest luminance values in the shadow, would appear completely white. Chetan Nandakumar suggested that we put this implication to the test, and we did that in Experiment 5. Using those factors shown in our prior experiments to maximize the perceived embeddedness of the disks, we conducted Experiment 5 using blurred disks, viewed successively, through a pinhole. 
Fifteen observers viewed the stimulus and judged the lightness of the seven disks in the shadow region using the Munsell chart. 
Matches in the shadow-only condition were compared to the matches for the disks in the shadow in the pinhole condition of Experiment 3 ( N = 15), the most similar whole image condition (although those disks were presented simultaneously). 
Results and discussion
Mean lightness matches for each disk are shown in Figure 8. In the shadow-only condition, the mean lightness of the lightest disk (disk 10) was Munsell 9.03 and the average lightness of all seven disks was Munsell 8.7 ( SE = 0.1), consistent with predictions of the anchoring theory. In Figure 8, the data are plotted in terms of log reflectance, but the white bar shows the range of white shades between Munsell 9.0 and 9.5. When compared to the disks in the whole image condition ( M = 1.74, SE = 0.04, also plotted in Figure 8), the disks in the shadow-only condition were significantly lighter ( M = 1.86, SE = 0.01), t(26) = 3.05, p < 0.01. 
Figure 8
 
Experiment 5: Lightness of the probe disks in the shadow framework. (Solid line) Shadow-only condition viewed successively through the pinhole. (Dotted line) Whole image condition viewed simultaneously through the pinhole. The region equivalent to white (Munsell 9.0–9.5) shown by the horizontal bar.
Figure 8
 
Experiment 5: Lightness of the probe disks in the shadow framework. (Solid line) Shadow-only condition viewed successively through the pinhole. (Dotted line) Whole image condition viewed simultaneously through the pinhole. The region equivalent to white (Munsell 9.0–9.5) shown by the horizontal bar.
In this comparison, the amount of the image (whole vs. shadow-only) is confounded with presentation mode (simultaneous vs. successive). However, in a separate control experiment not reported here, when the type of disks (blurred), mode of presentation (simultaneous), and viewing conditions (binocular) were kept constant, the disks in the shadow-only condition appeared significantly lighter ( M = 1.79, SE = 0.01) than those from a whole image condition ( M = 1.67, SE = 0.01), t(25) = 3.17, p < 0.01. 
General discussion
Probe disk technique
Our results illustrate the usefulness of probe disks even though the locations probed in this study were quite sparse. One could quite easily probe a very dense matrix of locations, thus producing a rather detailed mapping of computed lightness values across the entire image. 
Framework effect
Probing the lightness computation at 13 separate locations in the photograph Trastevere, we found a strong framework effect. That is, lightness values within either the sunlight region or the shadow region were roughly homogeneous, with a pronounced step function at the framework boundary. This result strongly implies that, in computing lightness values, disk luminance is evaluated relative to a different standard in the shadow, compared to the sunlight. 
The concept of frames of reference is closely associated with the gestalt school, particularly with Koffka (1935). Authors of structure-blind models tend to be wary of concepts like frames of reference, which they regard as not sufficiently concrete. While agreeing with the need for greater operationalization, we submit that our findings strongly suggest that the visual system does exhibit a framework effect that cannot be explained without an explicit representation of the structure of illumination in the scene. We are aware of no low-level approach that can account for our obtained pattern of results. 
A number of studies (Diamond, 1955; Heinemann, 1972; Kozaki, 1963; Newson, 1958; Stevens, 1967; Stewart, 1959) have reported stronger induction, or contrast, effects when the target area is smaller relative to the inducing area, which raises the question of whether the results we obtained in the perspective condition of Experiment 1 could be attributed to the altered disk sizes used in that condition. While some of the trends we obtained are consistent with such an interpretation, many are not. For example, disks 1 and 2 should appear lighter, and disks 12 and 13 should appear darker, in the perspective condition (where they are larger) than in the identical condition. Likewise, in the perspective condition, disks 7, 8, and 9 should be lighter than disks 12 and 13. These trends do not occur. 
Kingdom (2003) has claimed, without data, a larger simultaneous contrast effect using blurred targets. However, more often blur has been shown to have the opposite effect, as seen in Hering's (1874/1964) shadow/spot experiment. Data reported by MacLeod (1947) and Thomas and Kovar (1965) show that a blurred disk appears more similar in lightness to its background than does a sharp disk, which is consistent with the widely accepted view that a gradual luminance ramp appears to have less amplitude than a sharp edge of the same physical amplitude. The well-known Craik–O'Brien effect also demonstrates this. 
Skeptics may suggest that what we have attributed to frameworks in the image can be more simply explained by local contrast. Indeed all of our disks in the sunlight are decrements (darker than the immediate surround) while all of our disks in the shadow are increments. However, an appreciation of the image in Figure 9 shows that our results cannot be reduced to a matter of local contrast. Here we have placed five probe disks on Adelson's well-known checkered shadow illusion. Note that the upper right and lower right disks have the same local contrast (given that their background squares have the same luminance and that the disks are all equiluminant), yet they appear very different in lightness. Moreover, the upper three disks have very different local contrasts and yet they appear very similar in lightness. The same is true for the lower two disks. This image shows clearly that any effect of local contrast on lightness is small relative to the framework effect. 
Figure 9
 
Adelson's Checker shadow illusion with probe disks. The two rightmost disks have the same local contrast, but they appear very different in lightness. The three upper disks have very different local contrast, but they appear approximately the same in lightness. The same is true for the two lower disks.
Figure 9
 
Adelson's Checker shadow illusion with probe disks. The two rightmost disks have the same local contrast, but they appear very different in lightness. The three upper disks have very different local contrast, but they appear approximately the same in lightness. The same is true for the two lower disks.
Embeddedness
We hypothesized that, consistent with the anchoring theory, the size of the framework effect (defined as the difference between the average lightness values in the two frameworks) would be directly related to the perceived embeddedness of the disks. By perceived embeddedness, a variant of gestalt belongingness, we mean the degree to which the disks appear to belong to each framework, or the degree to which the disks appear to have been present in the scene when the photograph was taken. In Experiment 1, we increased perceived embeddedness by adding perspective to each disk consistent with the perspective of the scene at that location and by adding a slight blur to each disk consistent with the slight blur of the photograph. Each of these measures increased the strength of the framework effect. 
In Experiment 2, we decreased perceived embeddedness by pasting paper disks on the glass front of the computer monitor. As predicted, this weakened the framework effect, even though the paper disks had exactly the same luminance, color, visual angle, and background as the original disks. 
In Experiment 3, we increased the vividness of the depth in the scene by having subjects view the photograph through a pinhole. As expected, this method increased the framework effect even more, we believe, by weakening the global framework. 
Other perceptual groups
In Experiment 4, we presented the probe disks one at a time. With hindsight, we might have used this method throughout. When all 13 disks are present at the same time, they tend to form a weak perceptual group that might be called the disk group (or framework) based on similarity. Within that group, all disks would have the same lightness value, and as the highest (and only) value, it would be white. Thus, the disk group would tend to wash out the framework effect, by raising the lightness values of disks in the sunlight framework (in which they are middle gray) more than in the shadow framework (in which they are already white). Thus, when we prevented the formation of the disk group using successive presentation, we found both a stronger framework effect and generally lower disk lightness values. This implies that in all of our experiments except Experiment 4 our results understated the magnitude of the framework effect by about one Munsell step. 
In Experiment 2, the disks were not only grouped together by similarity, but because their perceived location in a slightly nearer depth plane further segregated them from the entire Trastevere photograph itself, and perceptually grouped them with other objects in the dimly lit laboratory. This further lightened the disks and reduced the framework effect. 
The core concept of the anchoring theory is that the perceived lightness of a target surface is a weighted average of at least two luminance ratios: (1) the ratio between the target luminance and the highest luminance in the target's immediate framework and (2) the ratio between target luminance and the highest luminance in the global framework. This general concept was first proposed by Kardos (1934), who called it codetermination. In addition to its fit with the empirical data, this concept offers a strong explanation for failures of constancy in lightness constancy experiments. In addition, it explains why our probe disks in the shadowed framework do not appear fully white, even though they have the highest luminance values in that framework. Codetermination implies that if the sunlight framework were eliminated, the disks would appear fully white. This prediction was tested in Experiment 5: when the sunlight framework was hidden, the disks did appear white. 
In recent years, several authors (Bloj et al., 2004; Boyaci, Doerschner, & Maloney, 2006; Boyaci, Maloney, & Hersh, 2003; Ripamonti et al., 2004) have proposed that lightness is computed by detecting the slant of a surface and then taking into account the intensity and direction of the light source. That approach is broadly consistent with our results. Though of course, as with the closely related approach taken earlier by Helmholtz, the details of exactly how the illumination is taken into account have not been spelled out. We believe we are offering a more operational description of how the illumination, in effect, is taken into account. We propose that the visual system simplifies the computation of lightness by perceptually grouping together patches of the image that represent equal levels of illumination. Such a group of patches constitutes what Koffka called a frame of reference, or framework, in terms of the anchoring theory. According to the anchoring theory, the lightness of each member patch is primarily computed based on the relationship of its luminance to the highest luminance in the framework. Notice, however, that this approach does not require an estimate of either the direction or intensity of the light source. Secondarily, however, some weight is also given to the relationship of the target patch to the highest luminance in the whole image. According to the concept of codetermination, the actual lightness percept represents a weighted combination of the lightness value computed within the local framework and the value computed within the global image. This hypothesized process does not produce 100% veridical lightness values, merely values consistent with human performance. 
Acknowledgments
This research was supported by grants from the National Science Foundation (BCS-0643827) and the National Institute of Health (BM 60826-02). The authors would like to thank Yoko Mizokami and Chetan Nandakumar for their inspiring suggestions, Edward H. Adelson for permission to reproduce and modify his Checker shadow illusion, as well as Jennifer Faasse, Simone Whyte, Steven Ivory, and Oscar Escobar for the their help in data collection. 
Commercial relationships: none. 
Corresponding author: Alan L. Gilchrist. 
Email: alan@psychology.rutgers.edu. 
Address: 101 Warren Street, Newark, NJ 07102, USA. 
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Figure 1
 
The reproduction of the photograph Trastevere (1959) by Henri Cartier-Bresson. Thin brackets on the side indicate the part of the image used as stimulus in Experiments 1, 3, 4, and 5. Bold brackets indicate the part of the image used as stimulus in Experiment 2.
Figure 1
 
The reproduction of the photograph Trastevere (1959) by Henri Cartier-Bresson. Thin brackets on the side indicate the part of the image used as stimulus in Experiments 1, 3, 4, and 5. Bold brackets indicate the part of the image used as stimulus in Experiment 2.
Figure 2
 
A schematic representation (not the actual stimulus) showing the locations of 13 probe disks on the photograph.
Figure 2
 
A schematic representation (not the actual stimulus) showing the locations of 13 probe disks on the photograph.
Figure 3
 
A sample of the stimulus showing (a) identical, (b) perspective, and (c) blurred probe disks.
Figure 3
 
A sample of the stimulus showing (a) identical, (b) perspective, and (c) blurred probe disks.
Figure 4
 
Experiment 1: Lightness of each probe disk in the identical (solid line), the perspective (dashed line), and the blurred (dotted line) conditions. Disk numbers correspond to locations marked in Figure 2.
Figure 4
 
Experiment 1: Lightness of each probe disk in the identical (solid line), the perspective (dashed line), and the blurred (dotted line) conditions. Disk numbers correspond to locations marked in Figure 2.
Figure 5
 
Experiment 2: Lightness of each probe disk in the paper (solid line) and the control (dashed line) conditions.
Figure 5
 
Experiment 2: Lightness of each probe disk in the paper (solid line) and the control (dashed line) conditions.
Figure 6
 
Experiment 3: Lightness of each probe disk in the pinhole (dashed line) and the binocular (solid line) conditions.
Figure 6
 
Experiment 3: Lightness of each probe disk in the pinhole (dashed line) and the binocular (solid line) conditions.
Figure 7
 
Experiment 4: Lightness of each probe disk in the simultaneous (solid line) and the successive (dashed line) conditions.
Figure 7
 
Experiment 4: Lightness of each probe disk in the simultaneous (solid line) and the successive (dashed line) conditions.
Figure 8
 
Experiment 5: Lightness of the probe disks in the shadow framework. (Solid line) Shadow-only condition viewed successively through the pinhole. (Dotted line) Whole image condition viewed simultaneously through the pinhole. The region equivalent to white (Munsell 9.0–9.5) shown by the horizontal bar.
Figure 8
 
Experiment 5: Lightness of the probe disks in the shadow framework. (Solid line) Shadow-only condition viewed successively through the pinhole. (Dotted line) Whole image condition viewed simultaneously through the pinhole. The region equivalent to white (Munsell 9.0–9.5) shown by the horizontal bar.
Figure 9
 
Adelson's Checker shadow illusion with probe disks. The two rightmost disks have the same local contrast, but they appear very different in lightness. The three upper disks have very different local contrast, but they appear approximately the same in lightness. The same is true for the two lower disks.
Figure 9
 
Adelson's Checker shadow illusion with probe disks. The two rightmost disks have the same local contrast, but they appear very different in lightness. The three upper disks have very different local contrast, but they appear approximately the same in lightness. The same is true for the two lower disks.
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